What is the advantage of carrying a net operating loss back against prior years income rather than forward against future years?

It depends on your situation whether it's actually an advantage or not. If your taxable income was higher in prior years than it's expected to be in the coming future years, then you're better off carrying it back. If your tax rate was lower in those prior years, you're better off electing not to carry it back and carrying it forward instead.

For example, let's say you generated an NOL in 2012 and had taxable income in 2010 and 2011, but your income was only taxed at a 10-15% rate. Let's say you expect a big turn around from what created that 2012 NOL and expect to be in a tax bracket of more than 15% in future years. In that case, you may be better off opting to carry an NOL forward.

Of course, for most folks the year of the NOL indicates a downturn and they don't know when the next upturn will be, so they're better off carrying it back (if there was taxable income in any of the carryback years). This would give them some tax relief now rather than later which may help boost their business, which was the reason for creating this law in the first place.